There is currently no effective chemotherapy for anaplastic carcinoma of the thyroid, which has a 50% survival of six months after diagnosis. Cell culture and mouse studies have shown that placlitaxel (taxol) is effective against anaplastic thyroid carcinoma. The current study is a multi-center Phase I/II looking at the effect of a 96-hour continuous infusion of taxol in patients with anaplastic thyroid carcinoma. Total accrual is expected to be 20 - 24 patients with 2 - 3 patients enrolled at each site.